Fri Nov 17, 2017
Wesley H. Holliday (UC Berkeley)
Possibilities for Boolean, Heyting, and modal algebras
In this talk, we describe an alternative to the standard representation theory for Boolean, Heyting, and modal algebras descending from Stone (1934, 1937) and Jónsson and Tarski (1951). While the standard theory leads to the well-known “possible world semantics” in logic, the alternative theory forms the basis of the recently investigated “possibility semantics” in logic. We will give an overview of this line of research, making connections to longstanding open problems and highlighting the contributions of University of California students.
The talk will be based on the following papers:
W. H. Holliday, “Possibility Frames and Forcing for Modal Logic,” 2015.
G. Bezhanishvili and W. H. Holliday, “Locales, Nuclei, and Dragalin Frames,” 2016.
G. Bezhanishvili and W. H. Holliday, “A Semantic Hierarchy for Intuitionistic Logic,” 2017.
N. Bezhanishvili and W. H. Holliday, “Choice-Free Stone Duality,” 2017.